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让我们先来看一个饶有趣味的问题: 例1 弟弟有20块巧克力糖,哥哥告诉他两种吃法:(一) 第一天吃5块,以后每天至少吃1块,但不能比前一天多,吃完为止;(二) 第一天吃糖数量不限,以后每天至少吃1块,但不能比前一天多,5天吃完。求证:按(一)、(二)两种吃法安排的方案一样多。证明图1的左边表示由(一)作出的一种方案:第一天吃5块,第二、三天各吃4块,第四天吃3块,第五、六天各吃2块。把该点阵绕对角线l翻转180°,得到右边的点阵,它表示了按(二)所作出的一种方案:第一、二天各
Let us first look at an interesting question: Example 1 The younger brother has 20 pieces of chocolate candy, and his brother told him to eat in two ways: (a) Eat 5 pieces on the first day, then eat at least one piece each day, but not before More than one day, after eating; (b) The amount of sugar on the first day is not limited, and at least one piece will be eaten every day, but no more than the previous day. Verification: There are as many formulas as the two methods of eating (a) and (b). The left side of Figure 1 shows a scheme made by (a): 5 on the first day, 4 on the second and third days, 3 on the fourth day, and 2 on the fifth and sixth days. Flip the dot matrix 180 degrees across the diagonal l to get the right dot matrix. It shows a scheme according to (ii): first and second days